The resistor is 2000?, the voltage of the battery is 10V and the value of the ca

Question

The resistor is 2000?, the voltage of the battery is 10V and the value of the capacitor is 1?F. The capacitor is initally uncharged and the switch is open. At time t = 0, the switch is closed.

Using Kirchhoff's loop rule and the definition of current, write down the differential equation that describes the charge on the capacitor as a function of time. Then prepare the equation for numerical integration using Euler’s method.

We can approximate the solution by treating time in discrete timesteps and using the following rule:

Write down your equation in this form.

Explanation / Answer

using kirchoff's loop rule:

V=i*R+(q/C)

as i=dq/dt

we get

V=R*(dq/dt)+(q/C)

==> 10=2000*(dq/dt)+10^6*q

==>dq/dt=5*10^(-3)-10^(-5)*q....(1)

hence q(n+1)-q(n)=(5*10^(-3)-10^(-5)*q(n))*delta(t)

where q(n) is charge magnitude at n the time point and q(n+1) is charge at n+1 th time point.

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